Variable Shape Cavitator Design for a Supercavitating Torpedo

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Variable Shape Cavitator Design for a
Supercavitating Torpedo
E. Alyanak, R. Grandhi, R. Penmetsa, V.
Venkayya Wright State University
10th AIAA/ISSMO Multidisciplinary Analysis and
Optimization Conference

• ONR Grant
• N00014-03-1-0057
• Dr. Kam Ng, Program Manager

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Outline

• Supercavitating torpedo and cavitator
  introduction
• Technique utilized for supercavity fluid modeling
• Cavitator Shape definition
• Optimization problem formulation
• Constraint discussion
• Modeling acceleration
• Results of the optimization problem
• Suggestions for a variable shape cavitator

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What is a Supercavitating Torpedoand a Cavitator?
Figures are artists impression
Figure From a Water Tunnel Test at Penn State
Cavity Water Vapor Bubble formation
behind the cavitator
Cavitator Initiates Cavity Formation
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Two-Phase Flow Analysis
Cavitation Number
Developed by Dr. Uhlman
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Cavitator Definition
Two Design Variables define the Shape with a
spline constructed through them
After the spline is created through the design
variables, any number of points can be created to
define the cavitator shape
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Cavitator Shape Optimization Formulation
Formulation
Constraint Behavior

• MinCD f(Shape Variables)
• Subject to

Cd
where
Cavity Number
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Cavity Growth and Torpedo Acceleration

• 0.6 x 10-6 (m2/s)
• U Velocity (m/s)
• D Cavitator Diameter

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Cavity Growth Vs Torpedo Acceleration
Cavitator Shape
Results P 0.75 thus
Velocity (m/s) Re L/D X1 X2 Flat Disk Flat Disk Optimized Shape Optimized Shape
Velocity (m/s) Re L/D X1 X2 Cd s Cd s
20 2.33E6 3 -0.3723 -0.2792 0.9278 0.4125 0.4739 0.3094
40 4.67E6 6 -0.3733 -0.2800 0.8017 0.2286 0.4019 0.1715
60 7.00E6 9 -0.3718 -0.2788 0.7564 0.1619 0.3785 0.1214
80 9.33E6 12 -0.3705 -0.2778 0.7326 0.1266 0.3669 0.0950
100 1.17E7 15 -0.3693 -0.2870 0.7177 0.1045 0.3478 0.0773
120 1.40E7 18 -0.3687 -0.2862 0.7072 0.0896 0.3435 0.0660
All Cavitator Shapes behave as a flat disk w.r.t.
cavity length and percent increase/decrease in
cavitation number
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Relaxation of s constraint
Optimization results for increasing velocity and
cavity length
Cavitator shapes
Increase in cavity length and velocity
Non-Dimensional Length
Non-Dimensional Length
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Suggested Shape Change
Cavitator profile for given cavity length
to
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Conclusion

• Modeled supercavitating flow
• Defined shape optimization problem to determine
  cavitator shape
• Solved optimization problem through the entire
  range of torpedo speeds
• Presented possible variable shape cavitator

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Thank You
E. Alyanak, R. Grandhi, R. Penmetsa, V.
Venkayya Wright State University
ealyanak_at_cs.wright.edu
10th AIAA/ISSMO Multidisciplinary Analysis and
Optimization Conference
ONR Grant N00014-03-1-0057 Dr. Kam Ng, Program
Manager